A transimpedance amplifier provides a near perfect loop current-to-voltage converter. It provides lots of gain while keeping your loop in wideband or short-circuit mode, which is what you need.
Our short story starts with a simple statement. A wideband receiving loop is a current-controlled voltage source. Think about it.
The voltage source we are seeking is something that will provide a signal into our receiver. Ideally, this voltage source is matched to our receiver 50Ω input and provides enough voltage for the receiver to do its magic Your controlling current is simply the current generated in your loop antenna by a magnetic field. So, your wideband receiving loop is just a transducer to convert magnetic field strength (amps per meter) into a received voltage.
In theory, you could achieve this by just placing a resistor across the loop terminals. Current from magnetic fields would then flow through this resistor with the loop in short circuit or wideband mode. An independent current flowing through a resistor (or impedance at AC) results in a voltage drop (V=IR). Voila, you have a signal to connect to your receiver.
But not so fast. In order for your loop antenna to work wideband, you must satisfy XL >> RLoad. This means that your load resistor must be very much smaller than the inductive reactance of the loop. I usually take “very much smaller” to mean at least an order of magnitude (10 times). Since the inductive reactance of my 1 meter loop antenna runs about 200Ω, this means that my load resister should be at least 10 to 20 times smaller, say 10Ω.
Since a 1 μV/m electric field strength produces roughly 9 nA of current, this passive loop current-to-voltage converter would produce V=IR or V=9nA*10Ω = 0.09 μV to my receiver. This is an S0 signal in the noise floor. Not useful. Looked at another way, the antenna has created a loss of around 20 dB.
So, how can we get some real decent signal from the loop antenna?
Loop Current-to-Voltage Converter – Transimpedance Amplifier
Your answer is an active conversion using a transimpedance amplifier, pictured above with a graphic from Wikipedia. This type of amplifier is perfect for performing loop current-to-voltage conversion while maintaining a low enough RLOAD to keep the wideband characteristics intact.
A transimpedance amplifier is a two-port device, with current flowing into port 1 and voltage out of port 2. Its transfer function, or transimpedance, is simply V=IR, or input current times the feedback resistance. You can implement this type of loop current-to-voltage converter using op amps or discrete circuits. Since the resistor is not loading the loop, you can select a much larger value to get more voltage gain.
The neat thing is that when inserted into the loop, a transimpedance amplifier looks pretty close to a short circuit. Which is exactly what you want to sniff and amplify the current while keeping XL >> RLoad. More on these later.